Problem: Recently Duff has been a soldier in the army. Malek is her commander.

Their country, Andarz Gu has n cities (numbered from 1 to n) and n - 1 bidirectional roads. Each road connects two different cities. There exist a unique path between any two cities.

There are also m people living in Andarz Gu (numbered from 1 to m). Each person has and ID number. ID number of i - th person is i and he/she lives in city number ci. Note that there may be more than one person in a city, also there may be no people living in the city.

<image>

Malek loves to order. That's why he asks Duff to answer to q queries. In each query, he gives her numbers v, u and a.

To answer a query:

Assume there are x people living in the cities lying on the path from city v to city u. Assume these people's IDs are p1, p2, ..., px in increasing order. 

If k = min(x, a), then Duff should tell Malek numbers k, p1, p2, ..., pk in this order. In the other words, Malek wants to know a minimums on that path (or less, if there are less than a people).

Duff is very busy at the moment, so she asked you to help her and answer the queries.

Input

The first line of input contains three integers, n, m and q (1 ≤ n, m, q ≤ 105).

The next n - 1 lines contain the roads. Each line contains two integers v and u, endpoints of a road (1 ≤ v, u ≤ n, v ≠ u).

Next line contains m integers c1, c2, ..., cm separated by spaces (1 ≤ ci ≤ n for each 1 ≤ i ≤ m).

Next q lines contain the queries. Each of them contains three integers, v, u and a (1 ≤ v, u ≤ n and 1 ≤ a ≤ 10).

Output

For each query, print numbers k, p1, p2, ..., pk separated by spaces in one line.

Examples

Input

5 4 5
1 3
1 2
1 4
4 5
2 1 4 3
4 5 6
1 5 2
5 5 10
2 3 3
5 3 1


Output

1 3
2 2 3
0
3 1 2 4
1 2

Note

Graph of Andarz Gu in the sample case is as follows (ID of people in each city are written next to them):

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 5, M = 1e7 + 5, K = 25;
struct query {
  int x, y, a;
};
query queries[N];
int sz[N];
bool done[N];
vector<int> g[N], qq[N], c[N];
set<int> marked;
int getSize(int node, int parent) {
  sz[node] = 1;
  marked.insert(node);
  for (auto child : g[node])
    if (child != parent && !done[child]) {
      getSize(child, node);
      sz[node] += sz[child];
    }
  return sz[node];
}
int getCentroid(int node, int parent, int total) {
  int bigChild, mx = 0;
  for (auto child : g[node])
    if (!done[child] && child != parent && sz[child] > mx)
      mx = sz[child], bigChild = child;
  if (mx <= total / 2) return node;
  return getCentroid(bigChild, node, total);
}
set<int> tmp;
vector<int> val[N];
int idxx[N];
vector<int> allNodes;
void dfs(int node, int parent, int idx) {
  allNodes.push_back(node);
  for (auto it : c[node]) {
    tmp.insert(it);
  }
  int cnt = 0;
  val[node].clear();
  idxx[node] = idx;
  for (auto it : tmp) {
    if (cnt > 10) break;
    cnt++;
    val[node].push_back(it);
  }
  for (auto child : g[node])
    if (child != parent && !done[child]) {
      dfs(child, node, idx);
    }
  for (auto it : c[node]) tmp.erase(it);
}
vector<int> ans[N];
void solve(int node) {
  allNodes.clear();
  tmp.clear();
  val[node].clear();
  idxx[node] = 0;
  for (int i = 0; i < min(int(c[node].size()), 10); i++)
    val[node].push_back(c[node][i]);
  for (auto it : c[node]) {
    tmp.insert(it);
  }
  allNodes.push_back(node);
  int cnt = 1;
  for (auto child : g[node])
    if (!done[child]) {
      dfs(child, node, cnt++);
    }
  for (int node : allNodes) {
    for (auto q : qq[node]) {
      query qu = queries[q];
      if (marked.find(qu.x) == marked.end() ||
          marked.find(qu.y) == marked.end())
        continue;
      if (idxx[qu.x] == idxx[qu.y]) continue;
      merge(val[qu.x].begin(), val[qu.x].end(), val[qu.y].begin(),
            val[qu.y].end(), back_inserter(ans[q]));
      vector<int> t;
      for (int i = 0; i < ans[q].size(); i++) {
        if (i == 0 || ans[q][i - 1] != ans[q][i]) t.push_back(ans[q][i]);
      }
      ans[q] = t;
    }
  }
  for (auto it : c[node]) tmp.erase(it);
}
void decompose(int node = 1, int parent = 1) {
  int centroid = getCentroid(node, parent, getSize(node, parent));
  solve(centroid);
  marked.clear();
  done[centroid] = 1;
  for (auto child : g[centroid])
    if (!done[child]) decompose(child, centroid);
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  for (int i = 1; i < n; i++) {
    int x, y;
    cin >> x >> y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  for (int i = 1; i <= m; i++) {
    int x;
    cin >> x;
    c[x].push_back(i);
  }
  for (int i = 1; i <= q; i++) {
    cin >> queries[i].x >> queries[i].y >> queries[i].a;
    qq[queries[i].x].push_back(i);
  }
  for (int i = 1; i <= n; i++) sort(c[i].begin(), c[i].end());
  decompose();
  for (int i = 1; i <= q; i++) {
    if (queries[i].x == queries[i].y) {
      int x = queries[i].x;
      for (int j = 0; j < min(10, (int)c[x].size()); j++)
        ans[i].push_back(c[x][j]);
    }
    cout << min(queries[i].a, (int)ans[i].size()) << ' ';
    for (int j = 0; j < min(queries[i].a, (int)ans[i].size()); j++)
      cout << ans[i][j] << ' ';
    cout << "\n";
  }
  return 0;
}